Hemispherical dielectric lens type antenna employing a uniform dielectric



343-75; OR 3550139 5R 1366.22, 1970 MGFARLAND Y 3,550,139

. HEMISPHERICALI DIELECTRIC LENS TYPE ANTENNA EMPLOYING A UNIFORM DIELECTRIC 7 Filed July 5, 1968 S Sheets-Sheet. 1

MATRIX SWITCHING I TR I RCVR 22 INVENTOR- JERRY L. McFARLAND BY 7 FIG. 2 XMTR z| W ATTORNEY Dec. 22, 1970 Filed July 5, 1968 J. L. M F'ARLAND HEMISPHERICAL DIELECTRIC LENS TYPE ANTENNA EMPLOYING A UNIFORM DIELECTRIC INCIDENT RAY 35 FIG. 3

3 Sheets-Sheet 3 RADIATED RAY 36 FIG. 5

INVENTOR. JERRY L. MCFARLAND ATTORNEY 1970 J. M FARLAND HEMISPHERICAL DIELECTRIC LENS TYPE ANTENNA EMPLOYING A UNIFORM DIELECTRIC 3 Sheets-Sheet 3 Filed July 5, 1968 240m 00 owJmmj :8 45.5% 222 8 02 8v zfim sou N50 I @000 I HlVd oaznvwaou INVENT'OR. (NOllVSN3dWO3 uauw g JERRY FARLAND ATTORNEY United States Patent 3,550,139 HEMISPHERICAL DIELECTRIC LENS TYPE AN- TENNA EMPLOYING A UNIFORM DIELECTRIC Jerry L. McFarland, Fullerton, Calif., assignor to North American Rockwell Corporation Filed July 5, 1968, Ser. No. 742,818 Int. Cl. H01q 19/06, /08

US. Cl. 343-754 24 Claims ABSTRACT OF THE DISCLOSURE BACKGROUND OF THE INVENTION In the art of microwave antenna design, dielectric lenses employing dielectric plastics such as polyethylene and polystyrene and the like, have been utilized to achieve focussing of a planar wave front (impinging on one side of the lens) at a focal point located on the other side of the lens. An advantage of such dielectric lens type antenna over the parabolic reflector or dish-type antenna is the relaxed mechanical and electric tolerances that may be employed. In other words, the reflected optics of a dish type antenna tends to double the effect of an error in the reflector shape, wherefor closer tolerances must be employed in a dish type design, relative to a dielectric lens type design of like aperture. An associated disadvantage is the attenuation incident to radiation through such dielectric lens.

A particularly useful type of dielectric lens for microwave application is the Luneberg lens, which is spherically symmetric and has the property that a plane wave incident on one side of the sphere is focused at a point on the other side of the surface of the sphere. Similarly, a transmitting point source located on the surface of the sphere is converted to a planar wave front on passing through the lens. Such property and reciprocal property are achieved by employing a spherical lens having a preselectively variable index of refraction. Such variable index of refraction, in practice, is approximated by constructing the lens of a series of mutually concentric dielectric shells of successively different discrete indices of refraction, referred to as a stepped-index Luneberg lens. Because of the spherical symmetry of the Luneberg lens, the focusing property thereof does not depend upon the direction of the incident wave. Accordingly, such lens may be used, in cooperation with an organ pipe scanner of switched feedhorns, in wide scanning-angle applications.

Another advantage of the full spherical Luneberg lens, relative to a dish type antenna, is the freedom from aperture blockage caused by the presence of the feedhorn in the reflective optic path of the dish type antenna. Although the antenna pattern of a Luneberg lens has a slightly narrower beamwidth than that of a parabolic reflector of the same circular cross section, the sidelobe level of the Luneberg lens is generally greater, due to the tendency of the ray paths in the lens to concentrate energy toward the edge of the aperture. In other words, the lens aperture amplitude distribution is not gabled or tapered. Another disadvantage of the full spherical Luneberg lens, relative to dish antennas, is the reduced efficiency, due to the dielectric losses and also due to scattering from the stepped indices of the discrete, mutually concentric dielectric elements.

Also a variable index Luneberg lens does not lend itself to feeding and phase-scanning a planar array. Because of the variable index property which is adapted for cooperation with only a point source, the aperture amplitude distribution is not stationary with changes in phase-scan, which results in spill-over losses as well as high side lobe levels. Moreover, the requirement of a variable index dielectric and the utilization of discrete dielectric elements of different indices of refraction present a design configuration which is expensive and somewhat less than convenient to manufacture.

A further and fuller discussion of Luneberg lens antennas is to be found in section 7.6 of the text Introduction to Rarar Systems by M. I. Skolnik published by McGraw-Hill Book Co. Inc. (1962). Such text suggests that a homogeneous dielectric sphere may be scanned through 41r solid radians if the index of refraction is not too high and if the diameter is not greater than about 30x. However, such set of structural limitations tends to limit the aperture size and aperture efliicency obtainable.

SUMMARY OF THE INVENTION By means of the concept of the subject invention, many of the above noted shortcomings in the prior art of Luneberg lens antennas tend to be overcome, while the inherent advantages thereof are retained.

In a preferred embodiment of the subject invention, there is provided a dielectric lens antenna, comprising a dielectric lens of a substantially uniform dielectric constant and shaped as a sector of a sphere representing a solid angle thereof less than and having a truncated apex. Microwave feedhorn means is arranged externally concentrically to and in cooperation with a spherical surface of the dielectric lens, whereby the lens surface formed by truncation of the apex forms a radiating aperture of the lens.

Compensatory shaping or curvature of the surface of the radiating aperture improves focusing, whereby a radiating point source or feed located at a selected point on the spherical surface of the lens provides a substantially planar wave front, propagating at an associated direction from the radiating aperture of the lens. An approximate quarter-wave plate formed upon the radiating aperture of the lens and having a dielectric constant of approximately the square root of that of the lens, provides impedance matching between the lens and free-space interface, whereby the aperture efliciency is improved. Also, the truncation of the dielectric lens reduces the attenuation through the lens.

Thus, in normal operation of the lens, beams may be propagated equally conveniently in a number of directions with less lens attenuation and increased aperture efficiency. Also, because a homogeneous dielectric is employed, the dielectric lens is cheaper and more convenient to fabricate than a variable-index Luneberg lens. Further, such homogeneous dielectric lens does not tend to concentrate the radiating rays therefrom at the edges of the aperture thereof, to the extent in the stepped-index or zoned Luneberg lens, and therefore demonstrates a lower sidelobe level.

The uniform index Luneberg lens of the invention provides a stationary amplitude distribution which does not change with changes in scan angle, and therefore lends itself to feeding and phase-scanning a planar array. Further, the device of the invention is not subject to the prior art limitation of an aperture not exceeding 30x, as indicated in Skolnik, but may employ much larger apertures 3 because of the aperture phase-tapering employed to overcome the limitations imposed by spherical aberration.

Accordingly, it is a broad object of the invention to provide an improved dielectric lens antenna.

It is another object of the invention to provide a scannable lens type antenna employing a dielectric lens having uniform dielectric properties.

It is still another object to provide a scannable dielectric lens antenna of reduced sidelobe performance and increased aperture efficiency.

These and further objects of the invention will become apparent from the following description, taken together with the accompanying drawings, in which:

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is an isomeric view illustrating a schematic a1- rangement in which the invention may be advantageously employed;

FIG. 2 is a schematic arrangement, partially in block form, illustrating further aspects of the system of FIG. 1;

FIG. 3 is a vertical section of the symmetrical antenna of FIGS. 1 and 2 and further illustrating the geometry thereof;

FIG. 4 is a graph of normalized path length error through the lens of FIGS. 1, 2 and 3 as a function of normalized aperture; and

FIG. 5 is an alternate embodiment of the invention employing a thinner lens.

In the figures, like reference characters refer to like parts.

DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring now to FIG. 1, there is illustrated a schematic arrangement in isometric view, of a system in which the o0 invention may be advantageously employed. There is provided a dielectric lens of a substantially uniform dielectric constant and being shaped as a sector of a hemisphere and having a truncating surface normal to an axis of symmetry 11, the spherical surface 12 of the sector representing a solid angle less than 180 and the truncating plane having a radius less than the radius of curvature of the spherical surface and defining a radiating aperture 13. In other words, lens 10 somewhat resembles the vessel of a cement mixer. Microwave feed means 14, comprising a plurality of feeds, is arranged externally concentrically of and in microwave circuit with the spherical surface. Adjacent the aperture 13 of lens 10 is a reciprocal radio frequency amplifying relay assembly comprising a first and second back-to-back matrix 16 and 17 or like feedhorns, a corresponding horn in each of matrices 16 and 17 being interconnected by a radio frequency amplifier of a third matrix of like radio frequency amplifiers 18, for amplifying a received signal wave front and relaying the amplified signal to lens 10 or for amplifying a signal wave front transmitted by cooperation of feed means 14 and lens 10. The construction and arrangement of such repeater-amplifiers is known in the art, one form of which being described for example in US. Pat. No. 3,039,089 issued June 12, 1962, to A. W. McMurtray, Jr., for Radar System. Uniform elements are preferably employed in each of matrices 16, 17 and 18 and arranged in order to avoid distorting the relative amplitude and phase distributions of the wavefronts of the signals translated or relayed thereby.

The cooperation of the arrangement of FIG. 1 in an exemplary directional communication link may be better appreciated from a consideration of FIG. 2.

Referring now to FIG. 2, there is illustrated a schematic arrangement partially in block form of a system utilizing the arrangement of FIG. 1. Hemispherical sector lens 10 is represented as a vertical central section, while the lens microwave feed means 14 is represented as an array of feedhorns 14a14n disposed in the plane of such central section. Matrices 16 and 17 (of radio relay means 15) are shown as that respective array of feedhorns 16a16n and 17a17n in the plane of the illustrated central section of lens 10, and RF amplifier matrix 18 is shown as an array of RF amplifiers 18a-18n.

There is further provided matrix switching means 19 such as an organ pipe scanner or other means for connecting a selected element of the plurality of feedhorns 14a14n through a transmit-receive switch 20 to one of a transmitter 21 and a receiver 22. In this way, the energy transmitted by transmitter 21 is made to be propagated in a desired phase front direction, and receiver 22 is made selectively responsive to phase fronts received from different directions by lens 10.

Because of the spherical optics employed by the lens of FIGS. 1 and 2, spherical aberrations are normally associated with attempted focusing of, say, a received planar wave front (from a selected direction) at a given feedhorn associated with such wave front direction. Accordingly, the truncating lens surface 13 of lens 10 is compensatorily shaped to provide improved collimation of microwave energy radiated therefrom and improved focusing of planar wave fronts received thereby. Such shaping of the aperture 13 relies on the fact that the refraction index of the dielectric lens 10 is different from that of free space and hence such shaped face (shown in much exaggerated form in FIG. 2 for ease of discernment) provides compensatory aperture phase distribution means. Such compensatory means have been employed as discrete elements in spherical reflector optical systems, to correct the spherical aberration occurring in a paraxial, incident collimated light beam or far-field image. Such discrete compensatory devices are referred to in the literature as Schmidt corrector plates, a description of which is to be found at pages 246-250 of the text Principles of Optics, by Born and Wolf, third edition, published by Pergamon Press, New York (1965).

In the device of the subject invention, the phase corrector plate is integral with and configured into the truncating surface 13 of dielectric lens 10. Also, the design of such compensatory curvature is selected to provide ideal compensation for wavefronts propagating at an angle intermediate a maximum scan angle of interest and a paraxial direction of axis 11, as to provide some degree of compensation at other angles. For example, in a lens having a spherical surface adapted to accommodate a half-angle scan of off axis, as shown more particularly in FIG. 3, the corrector surface may be configured to provide a best compensation for wavefronts arriving at an angle 30 off the paraxial direction. Such figuring of the lens aperture will yet provide an adequate degree of phase front compensation for phase front arrival angles less than and greater than the optimum angle, as to also accommodate paraxial direction (i.e., 0) and angles somewhat greater than the optimum angle of 30.

Referring to FIG. 3, for a feedhorn located at a point at a distance f from a hemispheric lens 10 having a radius of curvature R and an index of refraction n, it may be demonstrated that maximal flatness of a radiated wavefront at the radiating aperture, results for Such maximal flatness effect is yet not ideal, and includes some path length errors corresponding to aberration and astigmatism. In other words, the hemispherical lens is not perfecting focusing. Such path length error (6) or difference between maximal flatness and ideal flatness, may be reduced by means of the corrector plate figuring described above, in connection with the descriptions of FIGS. 2 and 3. Such path length error increases with aperlurc 2y (in FIG. 3).

The variation of normalized path length error (i/R as a function of normalized aperture y/R for an exemplary 90 lens having a nominal refractive index (11:20) is shown in FIG. 4, after corrector plate compensation for a scan angle of approximately 30. In such exemplary embodiment,

the normalized path length error fi/R is shown as a family of curves representing different scan angles: Curve 24 corresponds to the scan angle of 30 for which compensation is provided, and curves 25 and 26 correspond to scan angles of 45 and in the plane of scan, respectively. The path length error in the plane perpendicular to the scan plane is the same as the path length error labeled 0 scan, regardless of the scan angle. It may be seen from inspection of FIG. 4 that almost no path length error occurs in the plane of scan at the scan angle of 30 for which the corrector plate is configured to provide compensation, while a maximum (allowable) value of 0.0002 for the normalized path length error R occurs over the entire aperture and for all scan angles for a maximum normalized aperture y/R not exceeding 0.35.

The efficiency of the lens may be improved by reduction of reflections due to interface impedance mismatching. Such mismatching may be reduced at the interfaces 12 and 13 between lens and free space by a thin (approximately quarter wave) plate or layer 30, 31 of dielectric having a dielectric constant less than that of lens 10 and greater than that of free space, a preferred value being the square root of the value of that of lens 10 itself.

Accordingly, there has been described a focusing lens type antenna useful for Wide angle scanning applications. Side lobe levels in the radiation pattern may be reduced because the phase error or path length errors are small. The radius of curvature of such lens is not limited to 30 free space wavelengths (A), but may be constructed to be at least as large as 50A. Because of the improved wavefront flatness provided by the described lens antenna over a wide scan angle region, such device lends itself to cooperation with a reciprocal radio frequency amplifier relay. Further, because of the uniform dielectric constant employed for the lens, no aperture amplitude distribution errors or variations occur as a function of scan angle.

Although the device has been described as a scanning antenna employing switched multiple feeds, it is clear that a movable feed (moving concentrically of the spherical surface of the lens) may be employed. Also, such multiple feeds need not be switched but may be employed to provide a plurality of simultaneous beams having different directions. In other words, the beams may be generated either sequentially or simultaneously. Further, such multiple beam feeds may be applied to monopulse processors in angle tracking applications, and may employ polarization diversity techniques, since the polarization radiated by the lens is determined solely by that provided by the feed. Morreover, due to the difference in refractive index of the lens relative to free space, in cooperation with the collimated wavefront provided thereby, multiplication of the scan angle is achieved, as indicated by the angular difference between the incident and radiated rays 35 and 36 in FIG. 3.

The dielectric material employed by the lens of the inventions may be liquid, olid or gaseous; and may be real or artificial (i.e., a mixture of different materials representing two or more discrete indices of refraction, the mixture of different materials representing tWo or more discrete indices of refraction, the mixture having a uniform average value). Also, the aperture of the hemispherical lens may be located closer to the spherical surface thereof as to be provided a thinner lens, as illustrated in FIG. 5. In this way attenuation losses may be further reduced.

Accordingly, an improved wide-angle antenna has been described.

Although the invention has been described and illustrated in detail, it is to be clearly understood that the same is by way of illustration and example only and is not to be taken by way of limitation, the spirit and scope of this invention being limited only by the terms of the appended claims.

I claim:

1. An electronically scannable dielectric lens antenna comprising in combination:

a dielectric lens of a substantially unform dielectric constant and being shaped as a sector of a hemisphere having a truncating surface normal to an axis of symmetry, the spherical surface of said sector representing a solid angle less than and the truncating surface having a radius y less than the radius of curvature R of said spherical surface and defining a radiating aperture; and

a plurality of microwave feed means arranged externally concentrically of and in microwave circuit with said spherical surface of said lens,

said spherical surface and said aperture surface of said lens comprising interfaces.

2. The device of claim 1 in which there is further provided compensatory aperture phase distribution for improved collimation of microwave energy radiated from said aperture and improved focusing of planar wave fronts received by said aperture.

3. The device of claim 1 in which said truncating lens surface is compensatorily shaped for improved collimation of microwave energy radiating from said aperture and focusing of planar wave fronts received by said aperture.

4. The device of claim 1 in which there is further provided compensatory means for impedance matching at the interfaces of said lens and free-space.

5. The device of claim 1 in which there is further provided a substantially quarter-wave dielectric plate formed upon each of said interfaces of said lens and having a dielectric constant less than that of said dielectric lens and greater than that of free space.

6. The device of claim 1 in which there is further provided a substantially quarter-wave dielectric formed upon each of said interfaces of said lens and having a dielectric constant corresponding to approximately the square root of that of that dielectric lens.

7. The device of claim 1 in which there is further provided:

compensatory aperture phase distribution means for improved collimation of microwave energy radiated from said aperture, and

compensatory impedance matching means for improving the impedance match at the interfaces of said lens and free-space.

8. The device of claim 1 in which said truncating lens surface is compensatorily shaped for focusing at said feed means a planar wave front received by said aperture of said lens, and in which there is further provided a substantially quarter-wave dielectric plate formed upon each of said aperture and said spherical surface of said lens and having a dielectric constant less than that of said dielectric lens and greater than that of free space.

9. The device of claim 1 in which said truncating lens surface is compensatorily shaped for focusing at said feed means a planar wave front received by said aperture of said lens, and in which there is further provided a substantially quarter-wave dielectric plate formed upon said aperture of said lens and having a dielectric constant corresponding to approximately the square root of that of said dielectric lens.

10. The device of claim 1 in which the radial distance 7 of said microwave feed means from said spherical surface is defined by the relationship where R=radius of curvature of the spherical surface of the lens nzaverage index of refraction of the lens I and R are measured in the same units.

11. The device of claim 10 in which the value of )2 lies substantially within the range 1.53.

12. The device of claim 1 in which the ratio of the ra dius Y of said radiating aperture to said radius R of spherical curvature does not exceed .50.

13. The device of claim 1 in which there is further provided compensatory aperture phase distribution means for improved collimation of microwave energy radiated at paraxial and off-paraxial scan angles from said aperture and improved focusing of paraxial and off-paraxial planar wave fronts received at scan angles by said aperture.

14. The device of claim 1 in which said truncating lens surface is compensatorily shaped for improved c01- limation of microwave energy radiating at paraxial and off-paraxial scan angles from said aperture and improved focusing of paraxial and oIf-paraxial planar wavefronts received at scan angles by said aperture.

15. The device of claim 1 in which there is further provided:

compensatory aperture phase distribution means for improved collimation of microwave energy radiated at paraxial and off-paraxial scan angles from said aperture, and compensatory impedance matching means for improving the impedance match at the interfaces of said lens and free-space.

16. The device of claim 1 in which said truncating lens surface is compesatorily shaped for focusing at said feed means of paraxial and off-paraxial planar wavefronts received at scan angles by said aperture of said lens, and in which there is further provided a substantially quarter-wave dielectric plate formed upon each of said aperture and said spherical surface of said lens and having a dielectric constant less than that of said dielectric lens and greater than that of free space.

17. The device of claim 1 in which said truncating lens surface is compensatorily shaped for focusing at said feed means of paraxial and off-paraxial planar wavefronts received at scan angles by said aperture of said lens, and in which there is further provided a substantially quarter-wave dielectric plate formed upon said aperture of said lens and having a dielectric constant corresponding to approximately the square root of that of said dielectric lens.

18. A dielectric lens antenna comprising in combination:

a dielectric lens of a substantially uniform dielectric constant, the index of refraction, n, for which lies within the range 1.53, said lens being shaped as a sector of a hemisphere having a truncating surface normal to an axis of symmetry, the spherical surface of said sector representing a solid angle not exceeding 90 and the truncating surface having radius y defining a radiating aperture and the ratio of which to the radius of curvature R of said spherical surface not exceeding .50; and

microwave feed means arranged in microwave circuit with and externally concentric of said spherical surface for providing a beam pattern in a number of directions up to a maximum direction angle from said axis of symmetry said spherical surface of said lens by a radial amount f, the ratio of which to said radius of curvature does not exceed the factor 1/nl,

said spherical surface and said aperture surface of said lens comprising interfaces.

19. The device of claim 18 in which said truncating lens surface is compensatorily shaped for collimation of microwave energy radiating from said aperture at a direction intermediate said maximum direction angle and zero and for focusing of planar wave fronts received by said aperture from said intermediate direction.

20. The device of claim 18 in which said truncating lens surface is compensatorily shaped for collimation of microwave energy radiating from said aperture at a direction intermediate said maximum direction angle and zero and for focusing of planar wave fronts received by said aperture from said intermediate direction and in which there is further provided a substantially quarterwave dielectric plate formed upon each of said interfaces of said lens and having a dielectric constant corresponding to approximately the square root of that of said dielectric lens.

21. A dielectric lens antenna comprising in combination:

a dielectric lens of a substantially uniform dielectric constant and being shaped as a sector of a hemisphere having a truncating surface normal to an axis of symmetry, the spherical surface of said sector representing a solid angle less than 180 and the truncating surface having a radius y less than the radius of curvature R of said spherical surface and defining a radiating aperture; and

microwave feed means arranged concentrically of and in microwave circuit with said spherical surface of said lens,

said spherical surface and said aperture surface of said lens comprising interfaces, the center of said aperture surface positioned on the axis of symmetry from the center of curvature of said spherical surface a radial distance equal to or less than R from said spherical surface.

22. A dielectric lens antenna comprising in combination:

a dielectric lens of a substantially uniform dielectric constant and being shaped as a sector of a hemisphere having a truncating surface normal to an axis of symmetry, the spherical surface of said sector representing a solid angle less than 180 and the truncating surface having a radius y less than the radius of curvature R of said spherical surface and defining a radiating aperture; and

microwave feed means arranged concentrically of and in microwave circuit with said spherical surface of said lens, said feed means positioned a distance f from said spherical surface such that i R n1 where R is the radius of curvature of said spherical surface and n is the average index of refraction of said dielectric lens and where f and R are measured in the same units,

said spherical surface and said aperture surface of said lens comprising interfaces.

23. A dielectric lens antenna comprising in combination:

a dielectric lens of a substantially uniform dielectric constant and being shaped as a sector of a hemisphere having a truncating surface normal to an axis of symmetry, the spherical surface of said sector representing a solid angle less than 180 and the truncating surface having a radius y less than the radius of curvature R of said spherical surface and defining a radiating aperture; and

microwave feed means arranged concentrically of and in microwave circuit with said spherical surface of said lens,

said spherical surface and said aperture surface of said lens comprising interfaces, the center of said aperture surface being positioned on the axis of symmetry from the center of curvature of said spherical surface of a radial distance greater than a distance f and equal to or less than a distance R-i-f from said microwave feed means,

9 10 where: where R is the radius of curvature of said spherical R surface and n is the average index of refraction of f said dielectric lens and f and R are measured in the same units,

said spherical surface and said aperture surface of said lens comprising interfaces, the center of said aperture surface positioned on the axis of symmetry from the center of curvature of said spherical sur- R being the radius of curvature of the spherical surface of the lens, 11 the average index of refraction of the lens, R and f being measured in the same units. face a distance equal to or less than R from said 24. A dlelectric lens antenna comprising in combmh i l f ation:

said aperture surface center of said lens positioned a radial distance greater than the distance 1 and equal to or less than R+f from said microwave feed means.

of symmetry, the spherical surface of said sector 15 representing a solid angle less than 180 and the truncating surface having a radius y less than the radius of curvature R of said spherical surface and References Cited UNITED STATES PATENTS defining a radiating aperture; and 2415352 2/1947 Iams 343 911 microwave feed means arranged concentrically of and 2,669,657 2/1954 Cutler 343*911 in microwave circuit with said spherical surface of 3264648 8/1966 smdberg et 343 754 said lens, said feed rneans positioned a distance 1 3,321,763 5/1967 IkraFa et 343 754 from said spherical surface such that 3389394 6/1968 Lewis 343' 753 ELI LIEBERMAN, Primary Examiner i US. Cl. X.R. R n- 1 343777, 911 

